SUMMARY
Calculates the spectral estimate using the Power Density Spectra Method.
SYNTAX
PDS {[S]ECONDS v|[L]AGS n}, {[N]UMBER n}, {[T]YPE type}
where type is one of the following:
[HAM]MING | [HAN]NING | [C]OSINE | [R]ECTANGLE | [T]RIANGLE
INPUT
SECONDS v: Set the window length in seconds to v. LAGS n: Set the window length in lags to n. NUMBER n: Set the number of points to be used in the spectral estimate. TYPE type: Set type of window to be used. The advantages of each type is discussed in the writeup of the COR command.
DEFAULT VALUES
PDS TYPE HAMMING
DESCRIPTION
This command implements the "conventional" spectral estimator. It is the simplest the sample correlation function is first windowed with a correlation window, and the resulting function is transformed with an FFT to obtain the spectral estimate. As mentioned in the documentation on the COR command, there is a tradeoff between the bias of the estimate, primarily expressed in loss of resolution, and the variance of the estimate. As the window is made longer, the bias is reduced, since frequency-domain resolution is increased. However, the variance of the spectral estimate is increased, since the variance of the sample correlation function values is larger at larger lags. This occurs because fewer data points are used to estimate the values at larger lags.
The choice of correlation window type has a different effect than that of the choice of data window described in the COR documentation. It is a choice between two types of bias.
The spectral estimate approaches the convolution of the true spectrum with the Fourier transform of the correlation window. The window transform is characterized by a central lobe, which controls resolution, and sidelobes, which cause out-of-band power leakage. Typically one wants a narrow main lobe and small sidelobes. Large sidelobes tend to put an artificial, high regular "floor" on the spectral estimate, that can mask the rolloff of a spectrum with high dynamic range. The choice of window type trades off main lobe resolution against power-leakage through the sidelobes.
The rectangular window has the narrowest main lobe, and, therefore, the best resolution. However, it has the largest sidelobes. The cosine taper window reduces the sidelobes slightly without affecting the main lobe width much. These two windows were primarily included for estimating the spectra of transients, which requires little time-domain distortion. The Hamming and Hanning windows are popular windows which have small sidelobes and rather wide main lobes. They are useful when the user has a lot of data, and can control resolution by increasing the window size. Both are raised cosine windows, but the Hamming window is optimized to minimize the size of the largest sidelobe. It is generally to be prefered, and is the default window in this command. The triangular window also has rather good sidelobe structure, but has the especially desirable property that it guarantees that the spectral estimate will always be positive or zero.
Generally, PDS is to be prefered over the two parametric methods, MLM and MEM, when the user has a large data set available. This is because resolution is not constrained in that situation, and much more is known about this estimator than is known about the others. For example, the theory is available which allows us to estimate confidence limits, and the resolution of the method. Both of these diagnostics are included in SPE. The parametric methods generally exhibit better resolution than PDS, especially when estimating line spectra, and are more useful when a limited amount of data is available.
ERROR MESSAGES
- 5003: No correlatin function calculated.